Most solids expand when heated, a familiar phenomenon with many
practical implications. Among the rare exceptions to this rule,
the compound zirconium tungstate is especially unusual due to
the enormous temperature range over which it exhibits so-called
"negative thermal expansion," contracting as it heats
up and expanding as it cools, and because it does so uniformly
in all directions.

While engineers are already pursuing practical applications
in areas ranging from electronics to dentistry, physicists have
had a hard time explaining exactly what causes zirconium tungstate
to behave in such a bizarre manner. Now, a team of researchers
at UCSC and other institutions has reported new insights into
the atomic interactions underlying this phenomenon. A paper
describing their findings was posted online on November 22 and
appeared in the November 26 issue of the journal Physical
Review Letters.

"We have shown that a combination of geometrical frustration
and unusual atomic motions is likely to be important to the
negative thermal expansion in zirconium tungstate," said
Zack Schlesinger, a professor of physics at UCSC.

Geometrical frustration sounds like something a high school
math student might feel, but is actually a rich area of research
in physics and material science. In simple terms, geometrical
frustration is like trying to tile a floor with pentagons--the
shapes just won't fit together. In the case of zirconium tungstate,
geometrical frustration comes into play during certain temperature-related
vibrations of the compound's crystal lattice structure, the
configuration of atomic bonds that holds the atoms together
in a crystal.

The normal thermal expansion of solids results from changes
in the atomic motions that make up these lattice vibrations.
As heating adds more kinetic energy to the system, the lattice
structure expands (in most solids) to accommodate the increasingly
energetic atomic motions.

To study the atomic motions involved in lattice vibrations,
physicists separate the vibrations into discrete "modes"
or types of vibrations. In their investigation of zirconium
tungstate, Schlesinger and his collaborators found evidence
for a rotational ("twisting") mode that, due to geometrical
frustration, occurs together with a translational ("back-and-forth")
mode. This mixing of rotational and translational motion has
the effect of pulling the overall structure together as heating
puts more energy into the vibrations.

In other materials that show negative thermal expansion, the
vibrational modes that pull the solid together create instabilities
that eventually lead to rearrangements in the atomic structure.
As a result, the negative thermal expansion only occurs over
a narrow temperature range. In zirconium tungstate, however,
geometrical frustration appears to block any such instability.

At least, that is the researchers' current thinking, Schlesinger
said.

"To understand a complex system like this is not trivial.
You have to break it down into all the different components
of the atomic motions, and our work is making progress in that
direction," he said. "It involves both mathematical
analysis and experimental measurements, and ultimately you need
to be able to visualize it."

The experiments themselves are relatively simple, he said. They
involve shining infrared light on a sample of zirconium tungstate
and measuring the reflectivity, which can be transformed mathematically
into optical conductivity. These measurements reveal the frequencies
of light that are absorbed by coupling with the lattice vibrations,
and the researchers studied how these measurements changed with
temperature.

Schlesinger said he initially gave the project to an undergraduate
working in his lab, Chandra Turpen. When she began finding anomalous
results, graduate student Jason Hancock used mathematical modeling
to help figure out what the results meant.

"It started out as a senior thesis project that just became
a lot more interesting as we went along," Schlesinger said.

In addition to Schlesinger, Turpen, and Hancock, who is the
first author of the paper, the other coauthors are Glen Kowach
of the City College of New York and Arthur Ramirez of Bell Laboratories,
Lucent Technologies, in New Jersey.

Schlesinger said the findings are interesting with respect to
both pure physics and practical applications. On the pure physics
side, they seem to provide a new and unusual example of geometrical
frustration, which is most often studied in the realm of magnetism
and disordered systems such as spin glasses.

"This material is not disordered--it is a perfect stoichiometric
crystal--so we are seeing geometrical frustration manifested
in a whole new system," Schlesinger said.

On the practical side, thermal expansion is a big problem in
many different areas. In dentistry, most cracked fillings are
the result of uneven expansion and contraction--the so-called
"tea-to-ice-cream problem." And engineers working
on everything from electronics to high-performance engines must
cope with the effects of thermal expansion. A material that
did not expand or contract with changing temperatures would
have broad applications.

"If you could create the right mix of materials to neutralize
thermal expansion, that would be quite a significant technological
advance," Schlesinger said.

Additional information about this work, including an animation
of atomic motions in zirconium tungstate, is available on Schlesinger's
web site at physics.ucsc.edu/research/zs.html.